Math  /  Calculus

QuestionJump to Problem:[ 11 2 1]]
Problem 1. (1 point) Find yy as a function of tt if y(0)=5,y(0)=8y(t)=6y+33y=0\begin{array}{ll} y(0)=5, \quad y^{\prime}(0)=8 \\ y(t)= & 6 y^{\prime \prime}+33 y=0 \\ & \end{array}
Note: This particular weBWorK problem can't handle complex numbers, so write your answer in terms of sines and cosines, rather than using e to a complex power.

Studdy Solution
The solution to the differential equation is y(t)=5cos(112t)+8211sin(112t)y(t) = 5\cos\left(\sqrt{\frac{11}{2}}t\right) + 8\sqrt{\frac{2}{11}}\sin\left(\sqrt{\frac{11}{2}}t\right).

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